The influence of tensor forces on the differential cross section for the scattering of polarized neutron beams by protons.

Abstract

Tensor forces between two particles involve a dependence upon the angle between the direction of spin quantization and the line joining the two particles. The effect of tensor forces upon the scattering of a polarized neutron beam has been investigated theoretically. An expression has been obtained for the differential scattering cross section of the t r i p l e t states as a function of the polarization of both neutrons and protons. In general, this cross section i s also a function of the azimuthal angle to the direction of propagation of the neutron beam. The Influence of Tensor Forces on the Differential Cross Section for the Scattering of Polarized Neutron Beams by Protons Introduction In order to explain the electric quadrupole moment of the deuteron, i t has been necessary to introduce a tensor interaction potential of the form SV(r), where Rarita and Schvringer have calculated the effects of this potential upon both the bound and the unbound states of the neutron-proton system. In particular, they have calculated the scattering cross section of a beam of neutrons by a proton target for neutrons of low energy. These calculations were extended by Ashkin and Wu 3, who used a more general phase shift analysis. Recently, Rohrlich and Eisenstein ^ have solved the same problem (and obtained identical results'.) by means of a method which the authors find to be more satisfying theoretically. In a l l of the above papers, the protons and neutrons were 1. Rarita and Schwinger Physical Review 59, 436, 1941. 2. Rarita and Schwinger Physical Review 59, 556, 1941. 3. Ashkin and Wu Physical Review 73, 973, 1948. 4. Rohrlich andEisenstein Physical Review 75, 705, 1949. 2 considered to be completely unpolarized; i.e., the spins of the part i c l e s were assumed to have no preferential direction of alignment. The results of such a calculation showed the scattering cross section to be dependent only upon the polar angle to the direction of propagation of the neutron beam. However, i n order to answer a question raised by Dr. G.C. Laurence of Chalk River, i t was decided to investigate whether a dependence upon azimuthal angle i s introduced by certain polarization states of the neutron-proton system, and to determine how the polar dependence i s modified by such states. tering cross section as a function of the azimuthal andppoiar angles and of parameters which are determined by the polarization of the neutrons and protons. Calculation of the Differential Cross Section . applied to any singlet spin function, only the contribtuion of the t r i p l e t scattering to the total cross section w i l l be considered. In the centre of mass co-ordinate system, the i n i t i a l incident wave i s represented by the expression where r is the vector from proton to neutron, Hk is the momentum e=£ An expression has been obtained for the differential scatBecause the tensor interaction operator yields zero when